Domain-conditioned and Temporal-guided Diffusion Modeling for Accelerated Dynamic MRI Reconstruction

TL;DR

Dynamic MRI reconstruction remains challenging under undersampling. This paper introduces dDiMo, a diffusion-model framework that incorporates temporal information via $x$-$t$ and $k$-$t$ priors and adds a nonlinear CG refinement to recover time-resolved multi-coil data, applicable to both Cartesian and non-Cartesian acquisitions. Across cardiac cine and freely breathing lung imaging, dDiMo achieves higher PSNR/SSIM and better temporal alignment than state-of-the-art methods, demonstrating robust performance under varying undersampling factors. Limitations include relatively slow inference due to sequential diffusion steps, suggesting future work toward latent diffusion and subspace approaches to accelerate deployment.

Abstract

Purpose: To propose a domain-conditioned and temporal-guided diffusion modeling method, termed dynamic Diffusion Modeling (dDiMo), for accelerated dynamic MRI reconstruction, enabling diffusion process to characterize spatiotemporal information for time-resolved multi-coil Cartesian and non-Cartesian data. Methods: The dDiMo framework integrates temporal information from time-resolved dimensions, allowing for the concurrent capture of intra-frame spatial features and inter-frame temporal dynamics in diffusion modeling. It employs additional spatiotemporal ($x$-$t$) and self-consistent frequency-temporal ($k$-$t$) priors to guide the diffusion process. This approach ensures precise temporal alignment and enhances the recovery of fine image details. To facilitate a smooth diffusion process, the nonlinear conjugate gradient algorithm is utilized during the reverse diffusion steps. The proposed model was tested on two types of MRI data: Cartesian-acquired multi-coil cardiac MRI and Golden-Angle-Radial-acquired multi-coil free-breathing lung MRI, across various undersampling rates. Results: dDiMo achieved high-quality reconstructions at various acceleration factors, demonstrating improved temporal alignment and structural recovery compared to other competitive reconstruction methods, both qualitatively and quantitatively. This proposed diffusion framework exhibited robust performance in handling both Cartesian and non-Cartesian acquisitions, effectively reconstructing dynamic datasets in cardiac and lung MRI under different imaging conditions. Conclusion: This study introduces a novel diffusion modeling method for dynamic MRI reconstruction.

Figures (15)

• Figure 1: The overall framework of the proposed dDiMo, which integrates temporal information into the diffusion process for dynamic MRI reconstruction. (A) dDiMo performs progressive diffusion (forward process) or sampling (reverse process) of multi-coil dynamic k-space frames in the k-space domain, utilizing domain-conditioned and temporal-guided diffusion steps. (B) Each diffusion step incorporates a data consistency layer and includes several key components to adapt to dynamic image reconstruction: (1) A 3D CNN-based noise estimation network $\epsilon_{\theta}$ that captures spatial features within frames and temporal dynamics across frames, leveraging temporal coherence to learn denoising priors sensitive to temporal changes. (2) A 3D CNN-based $x$-$t$ network $\Psi_{\theta}$ that models temporal dynamics in the spatiotemporal image domain from intermediate denoised results $\hat{y}_{0|t}$, improving temporal alignment. (3) A 3D CNN-based $k$-$t$ network $\Phi_{\theta}$ that enforces MRI physics constraints through self-consistency learning in the ACS region of $k$-$t$ space, refining the denoising process and ensuring k-space consistency. (4) A nonlinear CG module that iteratively refines the reverse diffusion steps, adhering to physical constraints and enhancing robustness under challenging conditions.
• Figure 2: Schematic illustration of the use of $k$-$t$ priors during inference and training. (A) $k$-$t$ priors are derived from the ACS data in the $k$-$t$ space during training, guided by a self-consistency loss. (b) Self-consistency $k$-$t$ priors are applied to the input $\hat{y}_{0|t}^{'}$ during inference to enforce consistency in the frequency-temporal domain.
• Figure 3: The overall pipeline of the proposed dDiMo framework for non-Cartesian radial dynamic MRI reconstruction. (A) Example of continuously acquired multi-coil golden-angle radial k-space data. (B) Respiratory motion signals estimated from (a) are used for data sorting and binning into motion states. (C) Radial k-space data corresponding to each motion state, randomly selected during training, serves as the reference data. (D) Undersampled radial k-space data is generated within each motion bin of (C) using random undersampling patterns. (E-F) The radial data pairs are gridded to Cartesian k-space using the GROG algorithm. (G) The gridded data pairs are fed to the dDiMo framework for reconstruction.
• Figure 4: Qualitative comparison of different methods in spatial and spatiotemporal dimensions, along with corresponding error maps, for a cardiac cine in the short-axis view. Results are shown for undersampling rates of 4$\times$ (top), 8$\times$ (middle), and 16$\times$ (bottom). Spatiotemporal profiles along the yellow and red dotted lines are highlighted within yellow and red rectangles. The proposed method demonstrates superior performance in recovering fine structural details and preserving temporal coherence, even under highly undersampled conditions.
• Figure 5: Qualitative comparison of different reconstruction methods in spatial and spatiotemporal dimensions, accompanied by corresponding error maps, for cardiac cine in long-axis views: two-chamber (2CH), three-chamber (3CH), and four-chamber (4CH). Spatiotemporal profiles along the yellow and red dotted lines are highlighted within yellow and red rectangles. Results are presented for an undersampling rate of 4$\times$. Additional examples at undersampling rates of 8$\times$ and 10$\times$ are provided in Supporting Information Figure S1 and Figure S2, respectively. The proposed method demonstrates superior performance in recovering fine spatial details and preserving temporal dynamics, even under challenging undersampling conditions.